Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction
| dc.creator | Avishai, Y. | |
| dc.creator | Luck, J. M. | |
| dc.date | 2008-02-06 | |
| dc.date | 2008-03-21 | |
| dc.date.accessioned | 2026-07-07T09:44:06Z | |
| dc.date.available | 2026-07-07T09:44:06Z | |
| dc.description | This is the second of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. We investigate the problem of an electron subject to a spin-orbit interaction generated by the radial electric field of a static point charge sitting at the center of the sphere. The tight-binding Hamiltonian considered is a discretization on polyhedral graphs of the familiar form ${\bm L}\cdot{\bm S}$ of the spin-orbit Hamiltonian. It involves SU(2) hopping matrices of the form $\exp({\rm i}μ{\bm n}\cdot{\bmσ})$ living on the oriented links of the graph. For a given structure, the dimensionless coupling constant $μ$ is the only parameter of the model. An analysis of the energy spectrum is carried out for the five Platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron) and the C$_{60}$ fullerene. Except for the latter, the $μ$-dependence of all the energy levels is obtained analytically in closed form. Rather unexpectedly, the spectra are symmetric under the exchange $μ\leftrightarrowΘ-μ$, where $Θ$ is the common arc length of the links. For the symmetric point $μ=Θ/2$, the problem can be exactly mapped onto a tight-binding model in the presence of the magnetic field generated by a Dirac monopole, studied recently. The dependence of the total energy at half filling on $μ$ is investigated in all examples. | |
| dc.description | 25 pages, 15 figures, 12 tables. Various kinds of minor improvements | |
| dc.identifier | https://arxiv.org/abs/0802.0795 | |
| dc.identifier | http://arxiv.org/abs/0802.0795 | |
| dc.identifier | J. Stat. Mech. (2008) P06008 | |
| dc.identifier | doi:10.1088/1742-5468/2008/06/P06008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162751 | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.title | Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction | |
| dc.type | text |